Anachronism Stew: Perhaps only limited to the marketing, but the reveal trailer featured an extended "overture" for Jimi Hendrix's cover of "All Along The Watchtower", which, assuming it would even be written in this alternate history, was not even recorded in the real world until 1967; the game apparently starts in 1960.
Big Bad: Through initially thought to be Frau Engel, it's most likely Wilhelm "Deathshead" Strasse, who has been confirmed as the inventor of the Nazi's advanced war-winning weapons, and seen as though he was designated as "the most dangerous man in the Third Reich" many years ago
Bigger Bad: Probably Adolf Hitler or whoever is serving as Fuhrer assuming he's dead at that time. It is unknown if whoever leads the Nazis will be the Final Boss as in Wolfenstein 3D through.
BFG: A lot of the guns are designed this way, like this baby◊.
Continuity Nod: The prologue has you infiltrating Deathshead's latest lab, with disastrous results. Turns out he's increased security since the X-Lab and Zeppelin, and his latest Ubersoldaten cyborgs crush your whole squad to paste with ease.
Crapsack World: Well what do you expect with a Nazi Victory scenario being imposed on the entire world? And it is up to BJ to set things right.
Slightly more Justified than most examples, as these Mooks also seem to have a crude version of Power Armor, with the "Gasmasks" being a glorified faceplate.
Genre Throwback: For Old School FPS's, with things ranging from big levels to health packs to multiple weapon pick ups, though there is a bit of New School thrown in, like semi-regenerating health and a "cinematic" focus on the story.
Guns Akimbo: You can dual wield two of everything, like brandishing two massive shotguns or assault rifles, though you can't mix and match. Also, it takes twice as long to reload dual-wielded weapons, as B.J. reloads one gun, then the other.
Take Cover: Played with: B.J. can fire around corners, and even lean from one side to another on any turrets he's commanding (rather than stand up straight), but it's not snap-into-cover, and being able to maneuver quickly is a key part in staying alive.